x=3-1/2x=3/4(x-5)

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Solution for x=3-1/2x=3/4(x-5) equation:



x=3-1/2x=3/4(x-5)
We move all terms to the left:
x-(3-1/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-(-1/2x+3)=0
We get rid of parentheses
x+1/2x-3=0
We multiply all the terms by the denominator
x*2x-3*2x+1=0
Wy multiply elements
2x^2-6x+1=0
a = 2; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·2·1
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{7}}{2*2}=\frac{6-2\sqrt{7}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{7}}{2*2}=\frac{6+2\sqrt{7}}{4} $

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